Of course there is no special fool-proof technique to commit anything to long-term memory. It all depends on the user.

For me, I remember things better by being sure I understand the intricacies of what I'm doing. But because of this, without repeatedly doing problems, I can quickly forget the formulae that I need to use in tests. Except for long-term memory, it's always good to be able to know how to derive the formulae from first principles.

Are there any specific topics in maths you're having trouble remembering?

I'd learned directional derivatives and Lagrange multipliers about a month ago for an assignment and a test. I could do them pretty quickly, but to my disappointment, I found that I needed to go back to the formulas when trying to revise them recently.

I've probably also forgotten a lot of the linear algebra which I learned maybe three months ago.

I think knowing the principles will help (I seem to remember physics a lot better) but that said, I've also forgotten a lot of the trig identities which I'd learned by working through the proofs step-by-step.

Oh yes, of course. Forgetting something like how to manipulate algebraic expressions isn't common, but something as abstract as - say - expanding cos(a+b) can easily be forgotten. Unless you're one of the lucky few that CAN remember these after many months without revision, then good on you.

Else... do what we all do and study up to refresh your memory before the exam

I think that's natural. I tend to remember a lot of my trig identities because I spend a considerable amount of my time using them. But something like writing in spherical coordinates, I can't pull out those formulas out of my head, I have to sit and derive them every time.

So in general, I wouldn't worry too much about not remembering every detail on how to do everything, but rather on your ability to go back after some time and refresh yourself on how to do it.

For me it's pretty much a matter of how often I use whatever it is in question. When it's just for an exam or a few homework problems and you don't use it often after that, I don't know why you would commit it to long term memory! But when you use something many times in other courses, it gets dug in pretty good, and as far as I know that's the only sure way to do it.

After all, if you don't use it that often, why does it need to be committed to memory? It's unrealistic to think you can instantly recall everything you've ever learned. What's important is that when you run into something you don't immediately know how to do, you know where to look to get a quick refresher so that you do remember and can solve the problem or whatever. A professor of mine gave me this advice, and I have found it invaluable.

Learning techniques of higher math is more a matter of learning what references to use. When you use something frequently you will then learn it well. But not everyone uses everything commonly. What you need to do is to be able to go a reference and having used the technique before you should be able to get everything you need to apply it. Sometimes years will go by without having used some specific technique, it is always best to go to a reference then attempt to pull it out of the dusty corners of your mind.

The key is to want to learn it and know it for the rest of your life, not for the sake of doing well on the course or any other relatively short term goal. Like, imagine that you want to tell your grandkids about this, dunno if that example works but it should be that kind of mindset. I have a fair memory of almost everything, not perfect but fair. I can remember the outlines of any lecture in a subject I don't care about and haven't used ever since, not even on a test or so, a year after it went.
But by summoning my will to want to learn something I can push in a great deal of detail as well in the memory and it still stays indefinitely.

By the way, how rare are people who have really good memories? When I was younger I thought that everyone had a memory like me but the more I talk to people the more I notice that people in general forget just about everything they experience. Aside from family members I have just met two with exceptional memories like that, one which is a maths professor.

By the way, how rare are people who have really good memories? When I was younger I thought that everyone had a memory like me but the more I talk to people the more I notice that people in general forget just about everything they experience.

I would say I have quite a bad memory. Since I graduated and chanced discipline, my mathematics skill has suffered - a lot. From time to time I find that I need to revisit old calculus books, for instance, and revise the basics.

For me, the learning part is more than just remembering exactly what to you. When you understand how to do something, even if you forget it later down the line, you'll find that when you need to revisit the material it is very easy to pick up. For example, I find that I may be clueless in how to approach a particular problem but after a quick look at a calculus book the process comes flooding back. I have just enough snippets in my mind that all I need is a quick refresher to re-energise the pathway.